No paypal isn't a bank under American law meaning they aren't regulated or have to deal with the same rules as banks - this is the reason they can do those things not because of visa.
It's not a bank in America, though it is in other countries. It's a registered money transfer agent in most states, other names in others. Regardless, banks that offer merchant accounts do the exact same things, so how would it be different if PayPal were a bank? They'd be doing the same things, stemming from the same Visa policies.
